Question

If =18 SQ=18, =16QR=16, =14SR=14, =24TU=24, and =21VU=21, find the perimeter of △TUV. Round your answer to the nearest tenth if necessary. Figures are not necessarily drawn to scale.

Answer 1

To find the perimeter of △TUV, we need to determine the length of each of its sides.

First, we can use the information given to find the length of TU and UV. We know that =24TU=24 and =21VU=21, so:

TU = 24

UV = 21

Next, we can use the fact that SQ = SR and QR is given to find the length of SV. We know that =18SQ=18 and =14SR=14, so:

SQ + QR = SR

18 + QR = 14

QR = -4

Since QR is negative, we know that it must be measured in the opposite direction of SR. So we can write:

SR = SQ + QR = 18 - 4 = 14

Now we can use the fact that SV = TU - TV to find the length of TV. We know that TU = 24 and VU = 21, so:

SV = TU - VU = 24 - 21 = 3

Therefore, TV = SV + SV = 2SV = 2(3) = 6.

Finally, we can add up the lengths of all three sides to find the perimeter:

Perimeter = TU + UV + TV = 24 + 21 + 6 = 51

Therefore, the perimeter of △TUV is 51 units.